Demo 1D Flint

This notebook shows how to process 1D relaxation decays using Flint.

Importing Flint

To use Flint, we need to import it into our Python environment:

from pyflint.pyflint import Flint, FlintSignal
from pyflint.make_syntetic_data import time_distribution_signal_decay
import numpy as np

Generating syntetic data

For this demo, we will be working with a synthetic dataset generated by the function time_distribution_signal_decay, which is included with Flint. This dataset consists of a bimodal 1D T2 relaxation decay, and can be generated using the following cell.

Note that the amplitudes, centers, and widths arrays can be extended to generate more populations. The generated signal is saved in the signal_with_noise variable, while the T2 distribution is saved in the t2_distribution_intensity variable. We will be using these variables to demonstrate how to process 1D relaxation decays using Flint.

signal_time_axis, signal_with_noise, ILT_time_axis, t2_distribution_intensity = time_distribution_signal_decay(
        signal_num_points=64,
        signal_time_lim=[1e-4, 6],
        kernel_name="T2",
        normalized_noise=0.5e-4,
        t_dimension=500,
        t_axis_lim=[1e-4, 3],
        amplitudes=[0.5, 0.5],
        centers=[20e-3, 200e-3],
        widths=[5e-3, 50e-3],
        plot=True
    )

Processing data

Now that we have loaded our syntetic NMR data, we can use Flint to process it. We will start by converting the data to an NMRsignal class.

# load simulated NMR signal
flint_signal = FlintSignal.load_from_data(signal_with_noise, signal_time_axis)

Now we will set the parameters needed to perform the ILT:

• t1_range: The range of the first dimension relaxation time values to be used in the inversion. It is a numpy array with two elements, representing the minimum and maximum t1 values. In this demo, we use a range of [0.2, 3] seconds.
• kernel_name: The name of the kernel used. In this case "T2" kernel.
• kernel_dimensions: The dimensions of the kernel matrix used in the inversion. It is a list with two elements, representing the number of points in the t1 and t2 axes, respectively. In this demo, we use a kernel with 500 points in the t1 axis and 1 point in the t2 axis, as we are only considering 1D data.
• regularization_parameter: The value of the regularization parameter used in the inversion. It is a small positive number that helps to stabilize the inversion and avoid overfitting. In this demo, we use a regularization parameter of 1e-6.

# ILT parameters setting
t1_range = np.array([1e-3, 3e0])
kernel_dimensions = [256, 1]
regularization_parameter = 0.8e-2

# Calling Flint method
flint = Flint(flint_signal, kernel_dimensions, "T2", regularization_parameter, t1_range)
flint.solve_flint()
flint.plot()

Lipschitz constant found: 13694.605695420007